In this seminar, the participants will present a variety of classical results in the (widely understood) area of discrete mathematics (graph theory, additive number theory, discrete geometry, etc.) that have short elegant proofs. Among other sources, the topics will be selected from the books "The Art of Mathematics: Coffee Time in Memphis" by Bollobás and "Proofs from THE BOOK" by Aigner and Ziegler.

The seminar has no prerequisites, but it will be conducted in English.

B. Bollobás, The Art of Mathematics: Coffee Time in Memphis, Cambridge University Press, 2006

M. Aigner, G. Ziegler, Proofs from THE BOOK, 5th edition, Springer, 2014

March 1

Introduction; presentation of topics

March 8

Two problems about tiling rectangles

March 15

Sperner's theorem and the Littlewood–Offord problem

March 22

Bootstrap percolation in the integer lattice

March 29

Borsuk's conjecture

April 12

Three lemmas in additive combinatorics

May 3

The Kakeya problem over finite fields

May 17

The Erdős–Ko–Rado theorem and the chromatic number of the Kneser graph

May 24

Lattice paths and determinants

May 31

Three theorems in discrete convex geometry

June 7

Shannon capacity of C

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